1640–50; < Latin, plural of insigne mark, badge, noun use of neuter of insignis distinguished (by a mark); see in-², sign

Insignia, originally the plural of Latin insigne, began to be used as a singular in the 18th century, and the plural insignias appeared shortly thereafter. All uses— insignia as a singular or plural and insignias as a plural—are fully standard. The singular insigne still occurs, but insignia is more common.